The Sun says Liverpool and SGE have settled on a fee of £79m for the France U21 international.
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The breakdown will see Liverpool pay an initial £69m plus a further £10m due in bonuses.
Ekitike has already agreed terms over a six-year contract with the Reds.
A Liverpool medical is now being organised, with Ekitike to take his tests on Merseyside over the next 48 hours.
Last season, Ekitike scored 22 goals in 48 games last season to help Frankfurt qualify for the Champions League.